In my opinion, with 1 being the greatest, and down the line form there, the order would be..
1. Roman Empire (really, it's Rome, is there any competition?)
2. British Empire (at its height, controlled 25% of the world, but failed to exercise total power over it.)
3. Mongolian Empire (very large but was never completely united under one ruler, had much infighting)
4. Alexandrian Empire (could be the greatest empire considering the time frame it was created in, but also not the greatest considering the time frame it fell apart in.)
5. Ottoman Empire (A decently sized empire which lasted for many many years, but loses prestige from its later years being known as the 'sick old man' of europe.)
6. Napoleonic Empire (Napoleon was an eccentric genius, but he failed to dominate the English and was embarrassed by his invasion of Russia)
7. Austrian Empire (good in size but weak overall do to constant revolution.)
8. Aztec Empire (not Western-doesnt count.)
Your lists?
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